Does competition solve the hold-up problem?

In an environment in which both buyers and sellers can undertake match specific investments, the presence of market competition for matches may solve hold-up and coordination problems generated by the absence of complete contingent contracts. In particular, this paper shows that when matching is assortative and sellers' investments precede market competition then investments are constrained efficient. One equilibrium is efficient with efficient matches but also there can be equilibria with coordination failures. Different types of inefficiency arise when buyers undertake investment before market competition. These inefficiences lead to buyers' under-investments due to a hold-up problem but, when competition is at its peak, there is a unique equlibrium of the competition game with efficient matches - no coordination failures - and the aggregate hold-up inefficiency is small in a well defined sense independent of market size.